cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A007512 Primes of the form floor(e*10^k), i.e., formed by concatenation of an initial segment of the decimal expansion of e.

Original entry on oeis.org

2, 271, 2718281, 2718281828459045235360287471352662497757247093699959574966967627724076630353547594571
Offset: 1

Views

Author

N. J. A. Sloane, Robert G. Wilson v, Simon Plouffe

Keywords

Comments

The number of digits in a(n) is given in A064118. This allows us to get larger terms that cannot be displayed here, via the given FORMULA. Sequences A005042, A072952, A115453, A119343, A210704, ... are the analogs for Pi, gamma, sqrt(2), sqrt(3), 3^(1/3), ... - M. F. Hasler, Aug 31 2013

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Programs

  • Maple
    Digits := 110; n0 := evalf(E); for i from 1 to 100 do t1 := trunc(10^i*n0); if isprime(t1) then print(t1); fi; od:
  • PARI
    c=exp(1);for(k=0,precision(c),ispseudoprime(c\.1^k) & print1(c\.1^k,",")) \\ M. F. Hasler, Sep 01 2013

Formula

a(n) = floor(e*10^(A064118(n)-1)). - M. F. Hasler, Aug 31 2013

Extensions

Next term is a 1781-digit BPSW-probable prime 2718281828459045235...211151368350627526023. - Randall L Rathbun, Feb 02 2002
Edited by T. D. Noe, Oct 30 2008
Edited by M. F. Hasler, Aug 31 2013

A210704 Primes formed by initial digits of 3^(1/3) = A002581, i.e., of the form floor[3^(1/3)*10^k].

Original entry on oeis.org

144224957030740838232163, 144224957030740838232163831078010958839186925349935057754641619454168759682999733
Offset: 1

Views

Author

M. F. Hasler, Aug 31 2013

Keywords

Comments

Inspired by prime curios about 4957 (cf. LINKS), one of which honors the late Bruce Murray, 30.11.1931 - 29.8.2013.
See A210706 for the k-values. The keyword "less" for this records means that the next term (2488 digits) cannot be added / displayed here, and instead of listing further primes here, the k-values should be recorded in A210706.

Links

Crossrefs

Cf. A005042 (analog for Pi), A007512 (analog for e), A115453 (analog for sqrt(2)), A119343 (analog for sqrt(3)), A072952 (analog for gamma).

Programs

  • Mathematica
    With[{cr3=RealDigits[CubeRoot[3],10,100][[1]]},Select[Table[FromDigits[Take[cr3,n]],{n,100}],PrimeQ]] (* Harvey P. Dale, Mar 30 2024 *)
  • PARI
    (c=sqrtn(3,3),v=1/*set to 0 for indices instead of values*/)->for(k=0,precision(c),ispseudoprime(p=c\.1^k)&&print1([k,p][1+v]","))

Formula

a(n) = floor[A002581 * 10^A210706(n)], where A002581 is taken as a constant.

A072952 Primes obtained as initial segments of the decimal expansion of the Euler-Mascheroni constant gamma = 0.5772... .

Original entry on oeis.org

5, 577, 5772156649015328606065120900824024310421
Offset: 1

Views

Author

Shyam Sunder Gupta, Aug 12 2002

Keywords

Comments

The next term (a(4)) has 185 digits and is too large to include. - Harvey P. Dale, May 14 2013
Sequence A065815 gives the number of digits of a(n), resp. numbers k such that a(n) = floor(gamma*10^k). Sequences A005042, A007512, A115453, A119343, A210704, ... are the analog of the present sequence for Pi, e, sqrt(2), sqrt(3), 3^(1/3), ... - M. F. Hasler, Aug 31 2013
The original wording of the definition (and example) was "primes found in the decimal expansion..." which could as well refer to the sequence (5,7,7,215664901,5,3,2, ...) or (5,7,72156649, ...) or (5,7,7215664901, ...) (analogs to A047777 or A195834), or to the sequence (5,7,57, ...), analog to A198018. - M. F. Hasler, Sep 01 2013

Examples

			a(2) = 577, since 577 is the second prime obtained as initial segment of the decimal expansion of Euler-Mascheroni constant gamma = 0.577215664... .

Links

Crossrefs

Cf. A001620, A047777, A065815, A195834, A198018.
Analogous sequences: A005042 (Pi), A007512 (e), A115453 (sqrt(2)), A119343 (sqrt(3)), A210704 (3^(1/3)).

Programs

  • Mathematica
    nn=200;With[{emc=RealDigits[EulerGamma,10,nn][[1]]},Select[Table[ FromDigits[ Take[emc,n]],{n,nn}],PrimeQ]] (* Harvey P. Dale, May 14 2013 *)
  • PARI
    default(realprecision, 777); /* use that many digits */
A072952={(c=Euler, v=1/*set to 0 for indices (i.e., A065815) instead of values*/)->for(k=0, precision(c), ispseudoprime(p=c\.1^k)&&print1([k, p][1+v]", "))} \\ M. F. Hasler, Aug 31 2013
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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